>Just checking the pink changes... Mostly looks very good. I have
>one question and a comment.
>
>
>Section 3: I notice the condition:
>
> if x is in IP then IEXT(I(rdf:type)) contains <x, I(rdf:Property)>
>
>is relaxed from iff in the previous version. Do I take this to mean
>that some things of type rdf:Property (according to the relational
>extension of rdf:type) may be non-members of IP?
Yes. In general, there is no way prevent an interpretation from
having 'extra' structure, and we don't really want to, most of the
time. Something is in IP if its extension is nonempty, so not being
in IP can be interpreted as either not being a property or being a
property which has no values. There is no way to tell these apart by
looking at the assertions that use the property, and it would be
consistent to assert that PPP has rdf:type rdfs:Property even though
it had no property values. (Maybe someone else knows about its
values, for example....)
An alternative way to go would have been to have had a kind of
'negative' closure rule - a constraint- that said that any closure
which contains aaa rdf:type rdf:Property must also contain a triple
of the form bbb aaa ccc. But I didn't want to have 'rules' like that,
because then the whole notion of rule-closure goes out the window,
because you can't just apply the rules to exhaustion, there might be
many different closures, rdfs-entailment of subgraphs fails, and so
on.
BTW, I just realized that I had forgotten to change the corresponding
condition in the definition of rdfs-interpretation. Now fixed. The
summary table is also fixed to conform to this change.
>
>Section 4:
>
>RDF closure lemma. Any rdf-interpretation of E satisfies the
>rdf-closure of E; and any minimal simple satisfying interpretation
>of the rdf-closure of E is a satisfying rdf-interpretation of E.
>
>Er, shouldn't that be "Any *satisfying* rdf-interpretation of E ..." ?
>
>(Similarly section 6, RDFS closure lemma?)
Yes, it should. I often slip into this casual mode, sorry.
Fixed.
Also fixed date.
Pat
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